How can you split an edge in 3 or more edges?
First of all, go to Edit Mode and select the edge you want to split, then click the Subdivide button (step 1 in the picture below) and adjust the number of cuts in the panel that appears below (step 2). Also make sure you don't do anything else before adjusting the number of cuts, or the panel will disappear because Blender doesn't store that kind of information in its history, so even if you do Ctrl+Z the edge will return as it was before subdividing but the panel will not reappear and you'll have to do the procedure again.